Greg gets the prize behind door number one for the correct answer here.
The bore in the jamb, for the deadbolt, is about 3/8" off. you need to take a die grinder bit, chuck it in a small drill and oval the hole, toward the inside of the house, until the door closes tight with both the deadbolt AND the door latch engaged. It doesn't matter if you end up with a big ugly, egg shaped hole in this case. The door should be tightly sealed by the latch clicking into the strike, the deadbolt is secondary to the standard latch. Now you find yourself saying WTF is this guy talking about? What is a die grinder bit, and where is the die grinder bit store located? Well, I just did the Googles and found lots of pretty pictures and lot of dirt cheap ones on Amazon. Although you might find one at Lowe's or a real good local hardware place. Good luck, remember PPE, as in Personal protective equipment, safety glasses, cup, helmet, etc..... OK you can skip the helmet, and maybe the cup....... have fun.
So,